Isentropic Gas Research Articles

Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics

Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics

Experimental Investigation on the Performance of the Scroll Expander under Various Driving Cycles

Energy storage is considered a crucial unit in utilizing renewable energy sources, and compressed air energy storage (CAES) provides a cost-effective solution. It offers the benefits of zero pollution, a long lifespan, low maintenance costs, and minimal environmental impact. In order to increase the possibilities of compressed air energy storage for vehicle power, the performance of the expander needs to be studied. First, a CAES unit test bench is established. Then, the volumetric flow rate, rotational speed, torque, and output power are examined. Additionally, the isentropic exhaust temperature, pressure, and gas consumption rate of the scroll expander are analyzed. Finally, analyzing the economic feasibility of the CAES unit entails running the unit under varied driving conditions. Results reveal that the pressure of the input expander is high, which will lead to greater torque, greater peak power, and a greater temperature drop, but the gas in the air tank will also run out quickly. The peak power of the scroll expander does not occur at the maximum volume flow rate, rotation speed, and torque. The basic investment of the CAES unit mainly depends on the peak output power.

Исследование динамики свободной поверхности, ограничивающей конечную массу самогравитирующего газа

The work researches the evolution of the free surface which limits the polytropic, isentropic and self-gravitating ideal gas moving in vacuum. Gas currents are described with the mathematical model of gas dynamics, constructed due to the system of nonlinear integro-differential equations, expressed in Euler coordinate system. The transformation of the given system to the Lagrangian coordinates lets reduce it to the equivalent system consisting of integral Voltair’s equations and the equation of continuity in the Lagrangian form, and also it lets break down the unknown boundaries. Free boundary is determined as a great number of points of the system of integral equations solution achieved when depicting the boundary points of the initial area within the point of the moving area. For the system there is the proved theorem of the existence and uniqueness of the solution of the Cauchy problem in the space of the infinitely differentiated functions. Methods of qualitative research of the system of gas dynamics were applied in the work for the research of the evolution of the free surface.

Viscosity-flux approximation method to inhomogeneous system of isentropic gas dynamics

In this paper, we apply the maximum principle with the viscosity-flux approximation to obtain the a-priori L∞ estimates on the Riemann invariants of (1.1), Δ(νξ,ε,uξ,ε)≤ω(x−kt) and ϒ(νξ,ε,uξ,ε)≤ω(x−kt) for the solutions (νξ,ε,uξ,ε) of the Cauchy problem (1.6) and (1.7), where ω(x−kt) is a nonnegative bounded function, and to prove the global existence of the L∞ entropy solutions for the Cauchy problem of inhomogeneous system of isentropic gas dynamics (1.1) with arbitrary bounded initial data (1.2).

Pressurized green hydrogen from water electrolysis: Compression before or after electrolysis? A comparison among different configurations

Storing the intermittent renewable energy in the form of green hydrogen is the key pathway toward achieving a complete shift to renewable energy dependence. This study compared and examined various settings to produce hydrogen from water electrolysis, considering pressure and temperature effects over a broad range that covers both liquid and steam phases. Pressurized and atmospheric electrolysis at low and high temperatures were investigated under both isothermal and multistage isentropic post-electrolysis gas compression. Modeling and analysis based on established correlations and equations of state were used to estimate the system’s overall power requirements for each scenario. Increasing the operating temperature significantly reduced the electrolysis work while the pressure had an opposite effect, especially at low pressures. The results conclude that compressing liquid water, heating, then electrolyzing requires less overall energy than atmospheric electrolysis followed by product gases compression. This was valid for isothermal or isentropic compression despite the fact that the isothermal required the least work. The difference between pre-and post-electrolysis compression scenarios becomes greater at high pressure and temperature values. For instance, to obtain hydrogen at 25 °C and 50 bar, the power saving from pressurized electrolysis was 2.5% compared with atmospheric electrolysis followed by gas compression, which increased up to 20% at 600 °C and 200 bar. This indicates that high pressure steam electrolysis integrated with renewable systems leads to producing green hydrogen ready to store, transport, or use at less cost and complexities, especially with a cheap heat source or waste heat utilization.

The global existence of L∞$L^{\infty }$ solutions to isentropic Euler equations in general nozzle

AbstractIn this paper, we study the global entropy solutions for the Cauchy problem of the isentropic gas dynamics system in a general nozzle with bounded initial date. First, we apply for the flux‐approximation technique coupled with the classical viscosity method to obtain the estimates of the viscosity solutions. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework for any adiabatic exponent .

Numerical Study of Plasma Behavior and Power Generation Characteristics in a Disk MHD Generator With Xenon-Seeded Neon Gas

Plasma behavior and power generation characteristics in a disk-shaped magnetohydrodynamic (MHD) power generator with xenon (Xe)-seeded neon (Ne) working gas have been examined by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $</tex-math> </inline-formula> 2-D numerical simulation under the assumptions of isentropic gas flow and a non-MHD interaction. The seed fraction (mole% of Xe in the mixture) is varied from 0.0% (pure Ne) to 100.0% (pure Xe) to assess the effect that Xe seeding has on plasma behavior and power generation characteristics. Adding a small amount of Xe to Ne improves the power performance due to the resulting enhancement of electrical conductivity, whereas adding an excessive amount (over 5.0%) deteriorates the performance. At an appropriate load resistance, uniform plasma structure occurs for low seed fractions. However, the plasma structure becomes nonuniform for excessively high seed fractions (over 5.0%). This result suggests that adding an excessive amount of Xe can reduce the uniformity of the plasma structure in the generator. On the other hand, at low load resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&lt;$</tex-math> </inline-formula> the appropriate load resistance) and high load resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt;$</tex-math> </inline-formula> the appropriate load resistance), a nonuniform plasma structure occurs for any seed fraction and results in the deterioration of generator performance. The electron temperature ranges for maintaining uniform plasma structure become narrower as the seed fraction increases which can be attributed to the low ionization potential of Xe and its large atomic weight.

Multi-dimensional optimal system and conservation laws for Chaplygin gas Cargo-LeRoux model

The well-known Cargo-LeRoux model for the isentropic Chaplygin gas is investigated using classical Lie symmetry method. Optimal systems up to six dimensions are constructed using the adjoint transformation and the invariants of the admitted Lie algebras. We develop exact solutions to the Cargo-LeRoux model by using the one-dimensional optimal system and discussed the physical behavior of such solutions graphically. Conservation laws to the governing equations are also obtained by using the nonlinear self-adjointness of the model. The performance of the developed solutions is explored through the evolutionary behavior of a discontinuity wave.

Application of invariants of characteristics to construction of solutions without gradient catastrophe

The one-dimensional system of equations of isentropic gas dynamics is considered. First-order invariants of characteristics of this system are classified. Second-order invariants of characteristics are classified for polytropic processes. The infinite sequence of Darboux integrable systems is described. The approach to construction of smooth solutions without gradient catastrophe is proposed. Examples of solutions without gradient catastrophe are presented.

Vanishing Magnetic Field Limits of Solutions to the Isentropic Chaplygin Gas Magnetogasdynamics Equations

Vanishing Magnetic Field Limits of Solutions to the Isentropic Chaplygin Gas Magnetogasdynamics Equations

Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish

This paper is concerned with the Riemann problem for the isentropic Chaplygin gas magnetogasdynamics equations and the formation of $$\delta $$ -shocks and vacuum states as pressure and magnetic field vanish. Firstly, the Riemann problem of the isentropic magnetogasdynamics equations for Chaplygin gas is solved analytically. Secondly, it is rigorously proved that, as both the pressure and the magnetic field vanish, the Riemann solution containing two shocks tends to a $$\delta $$ -shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted $$\delta $$ -measure which form the $$\delta $$ -shock; while the Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the transport equations if we do not consider the virtual velocity in the vacuum region, the intermediate state between the two contact discontinuities is a vacuum state. Moreover, we also give some numerical simulations to confirm the theoretical analysis.

Global structure of two dimensional Riemann solutions to the Euler system for isentropic Chaplygin gas

AbstractIn this paper, we study the two dimensional Riemann problem of the Euler system for isentropic Chaplygin gas, and the initial data consist of three pieces constant states divided by an inverted Y‐type curve. The results extended the results in Chen and Qu where the solution of every one dimensional Riemann problem contains no slip plane. We divide the discussion into several cases and for each case, we give the structure of the solution containing slip planes by the method of generalized characteristic analysis.

Translationally invariant exact steady flows of gas and fluid

Abstract New exact 3-D steady translationally invariant (or z-invariant) flows of isentropic gas and ideal incompressible fluid are constructed. New exact solutions for steady magnetohydrodynamics equations are derived. We show that Euler equations for steady z-invariant flows of isentropic gas are equivalent to a coupled system of a partial differential equation of second order for the streamfunction ψ(x, y) which contains an arbitrary differentiable function H(ψ) and a transcendental equation connecting gas density ρ(x, y) with function ψ(x, y) and depending on equation of state p(ρ) = cρ γ and on the function H(ψ). We prove that functions ψ(x, y) and ρ(x, y) satisfy a universal nonlinear equation that is independent of equation of state p = p(ρ) and of the function H(ψ).

Global Existence of a Solution for Isentropic Gas Flow in the Laval Nozzle with a Friction Term

We are concerned with isentropic gas flow in the Laval nozzle with a friction term due to viscosity. It is well known that the flow attains the sonic state at the throat, where the cross section is minimum in the Laval nozzle. However, the present friction term changes the position of the sonic state into downstream, which is called chooking. Our goal in this paper is to investigate these phenomena mathematically. From the mathematical point of view, the friction term is different from normal friction terms such as $-\alpha m$ and difficult to treat with. In spite of its physical importance, the friction term has not received much attention until now. For the case without the friction term, the global existence of a solution was obtained by the author. However, for the case with the friction term, there are only restrictive results. The most difficult point is to obtain the bounded estimate of solutions. To solve this problem, we introduce an invariant region depending on the mass. Adjusting the invariant region, we invent a new difference scheme, which yields approximate solutions including the mass.

Euler equations for isentropic gas dynamics with general pressure law

In this work, we explore the limiting behavior of Riemann solutions to the Euler equations in isentropic gas dynamics with general pressure law. We demonstrate that in the distributional sense the delta wave of zero-pressure gas dynamics is formed by a limit solution. Finally, to present the concentration phenomena, we also offer some numerical outcomes.

Global weak solutions to the Euler-Vlasov equations with finite energy

This paper concentrates on the global existence of weak solutions in Lp with finite energy to a type of one-dimensional compressible Euler-Vlasov equations, which models the interaction between the isentropic gas and dispersed particles. Approximate solutions are constructed by adding artificial viscosity. Then the uniform Lp estimates of the approximate solutions with respect to the artificial viscosity are established through some subtle analysis on level sets of density and relative velocity. The convergence of approximate solutions to the desired weak solutions is guaranteed by the Lp compensated compactness framework.

Stability properties of the steady state for the isentropic compressible Navier–Stokes equations with density dependent viscosity in bounded intervals

We prove existence and asymptotic stability of the stationary solution for the compressible Navier-Stokes equations for isentropic gas dynamics with a density dependent diffusion in a bounded interval. We present the necessary conditions to be imposed on the boundary data which ensure existence and uniqueness of the steady state, and we subsequent investigate its stability properties by means of the construction of a suitable Lyapunov functional for the system. The Saint-Venant system, modeling the dynamics of a shallow compressible fluid, fits into this general framework.

Global existence to a diagonal hyperbolic system for any BV initial data

In this paper, we study the existence of solutions for a diagonal hyperbolic system, that is not necessarily strictly hyperbolic, in one space dimension, considering discontinuous BV initial data without any restrictions on the size of its norm. This system appears naturally in various physical domains, particularly in isentropic gas dynamics and dislocation dynamics in materials. In the case of strictly hyperbolic systems, an existence and uniqueness of a discontinuous solution result is available for BV initial data with small norm, whereas several existence and uniqueness results have been presented for non-decreasing continuous solutions. In the present paper, we show the global in time existence of discontinuous viscosity solutions to a diagonal hyperbolic system for every initial data of bounded total variation, without the assumption that the system is strictly hyperbolic. Up to our knowledge, this is the first global existence result of large discontinuous solutions to this system.

The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field

Abstract We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

Global Solutions to Isothermal System with Source

In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.